In CT X-ray imaging, a slice of a subject is imaged by irradiating it with X-rays in an X-ray beam emanating from an X-ray source in the plane of the slice. X-rays are incident on the slice along an edge of the slice which faces the X-ray source and pass through material in the slice. The material in the slice attenuates the beam by absorbing and scattering X-rays. The slice thus shadows the beam and the amount by which the beam is attenuated is a function of the amount and composition of the material in the slice and the energy spectrum of the X-ray beam.
Downstream of the slice, X-rays not absorbed or scattered, are detected by small aperture X-ray detectors, closely packed side by side, along an arc or in a complete circle, in the plane of the slice and oriented facing the X-ray source. Each detector measures the intensity of X-rays that have reached it after traversing a narrow tubule of material in the slice that lies along the line projected from the X-ray source to the detector. Each detector thus measures the attenuation of the beam resulting from the composition and density of all the material in the tubule. The cross sectional area of the tubule is substantially equal in size and shape to the size and shape of the X-ray beam spot on the aperture of the X-ray detector.
If I.sub.0 is the intensity of X-rays that enter a tubule at its upstream end and I is the intensity of the X-rays exiting the tubule at its downstream end, then I=I.sub.0 exp(-.intg..mu.(l)dl) (ignoring dependence of absorption on X-ray energy), where the integral is taken over the length of the tubule, and .mu.(l) is the absorption coefficient per centimeter for X-rays, in the material of the tubule at point l along the tubule. Since I.sub.0 is known and I is measured by a detector then ln(-I/I.sub.0)=.intg..mu.(l)dl and the X-ray intensity measurement at the detector is in effect a measurement of .intg..mu.(l)dl, hereafter an "attenuation measurement", for a tubule of material in the slice.
In medical CT imaging, the absorption coefficient .mu. of a material is commonly measured in CT units which is the absorption coefficient of the material relative to the absorption coefficient of pure water which is assigned a CT number equal to 0. Soft tissues commonly have CT numbers in the range from -1000 to 500, bone CT number is about 800, and metals often have CT numbers in excess of 2000.
A subfan angle is defined as the angle of the position of the X-ray source around the slice, measured from some convenient base line in the plane of the slice, from which the slice is irradiated. For a given subfan angle attenuation measurements are made for a large number of closely packed non overlapping tubules through the slice. The tubules are essentially contiguous and their number is large enough so that, at the given subfan angle, almost all points in the slice fall within a tubule and attenuation measurements are made for substantially the whole volume of the slice. The angle that a particular tubule makes with the base line when an attenuation measurement is made is called a view angle of the tubule. Each attenuation measurement is therefore identified by a view angle, and the particular tubule at the view angle, for which the attenuation measurement is made.
It is convenient to label the tubules with an index number that identifies the detector in the detector array which measures the X-rays transmitted through the tubule. Let the detectors in the detector array in the plane of the slice be labeled by consecutive increasing integers i=1,2, . . . N according to increasing displacement from detector "1". Then if the view angle is .theta., the attenuation measurements can be written as a function of i and .theta., in the form A(i,.theta.).
A set of attenuation measurements A(i,.theta.), is generally acquired for N tubules at each of many closely spaced subfan angles around a slice, from 0 to 180 degrees or from 0 to 360 degrees. Before reconstruction into an image, the acquired data from all the subfan angles is generally rebinned and organized into sets of data comprising N attenuation measurements for parallel tubules at a same view angle. The set of N measurements at a particular view angle is called a view. The set of views for all view angles around the slice at which data was acquired is called a projection set for the slice. From the projection set a map of the X-ray absorption coefficient of the material in the slice as a function of position in the slice can be determined. This map shows different structural features inside the slice. By mapping the absorption coefficient in this way for many slices, a three dimensional picture of the internal structures of the subject can be constructed.
There are a number of different algorithms and many different variations of algorithms that are used for processing attenuation data to construct a CT image of a slice irradiated by X-rays. A problem that continuously arises with image construction algorithms commonly used for medical CT imaging, is that objects that have sharply defined boundaries and high CT numbers compared to the CT numbers of surrounding body tissues are poorly imaged and give rise to artifacts in the constructed CT image. These artifacts distort and degrade the image. Examples of such objects are surgical clips, metal prosthesis and implants, dental fillings, or metal objects that have penetrated the body as a result of accident or violence, hereafter "metal inserts". Metal inserts typically give rise to artifacts called starbursts which comprise patterns of bright and dark bands emanating from the dense object. The artifacts typically comprise streaks across the constructed CT image which degrade and obliterate detail. As a result of such artifacts, important information, such as whether a bullet is touching the spinal column or a major artery, or how much clearance there is between an implant and a vital organ, cannot be accurately assessed.
Procedures have been developed to ameliorate these artifact effects by replacing or modifying attenuation data for tubules that pass through a metal insert in an imaged slice. Many of these procedures define "rub out" regions in the projection set data for the slice. Data from tubules passing through the rub out regions is discarded and replaced with data interpolated from attenuation data from tubules outside of and adjacent to both sides of the rub out regions. This "rub-out" of data, in effect, throws away the data from the offending metal insert and removes the metal insert from the constructed CT image. While this improves the image, information about the metal insert is discarded, and the relation of the metal insert to structures and tissues in the body, that is often important, is not imaged.
U.S. Pat. No. 4,590,558, to Gary H. Glover et al describes removing artifacts from a CT image of a subject which artifacts are caused by a high density object present in the subject. As described in this patent, in order to remove or reduce the artifacts, data from the high density object is removed from a rubout region of the projection set of the subject. This, in effect, removes or reduces the artifacts in the image caused by the object, by removing the object.
U.S. Pat. No. 4,709,333, to Carl R. Crawford, describes a similar approach for the case where two high density objects are present in an imaged subject. In this patent a method is presented for removing data resulting from the two high density objects at regions of a projection set of the subject where the two objects shadow each other. As in the above patent artifacts are removed by removing the objects causing them.
Other techniques use iterative methods to correct CT images for the presence of artifacts resulting from metal inserts present in an imaged slice. Some of these techniques do not delete the metal insert from the constructed CT image of the slice but they are generally computationally complicated and often require many iterative steps. Such an iterative method is disclosed in U.S. Pat. No. 5,243,664 to Heang K. Tuy.
It would be desirable to have a computationally inexpensive algorithm that reduces artifacts in a CT image of a slice of a subject that are caused by metal inserts present in the slice, without removing the metal inserts from the image.